Academic Catalog

Mathematics

Courses

Sets, functions and graphs, exponents, polynomials and algebraic equations, systems of equations.
Prerequisite(s): One year of high school algebra.

MTH 114. Contemporary Mathematics. 3 Hours

Study of contemporary mathematical topics and their applications. Topics may include management science, statistics, social choice, size and shape, and computer mathematics.
Prerequisite(s): Two years of high school algebra.

MTH 116. Precalculus Math. 4 Hours

Review of topics from algebra and trigonometry including polynomials, functions and graphs, exponential and logarithmic functions, trigonometric functions and identities.
Prerequisite(s): Two years of high school algebra.

MTH 128. Finite Mathematics. 3 Hours

Topics from mathematics used in business including systems of equations, inequalities, matrix algebra, linear programming and logarithms; applications to compound interest, annuities and other finance problems.
Prerequisite(s): MTH 102 or sufficient college preparatory mathematics.

MTH 129. Calculus for Business. 3 Hours

Topics from differential and integral calculus used in business; applications to optimizing financial functions, marginal functions in economics, and consumer or producer surplus.
Prerequisite(s): MTH 128 or sufficient college preparatory mathematics.

MTH 137. Calculus I with Review. 4 Hours

Introduction to the differential and integral calculus with an extensive review of algebra and trigonometry; differentiation and integration of algebraic and transcendental functions with applications.
Prerequisite(s): Two years of high school algebra.

MTH 138. Calculus I with Review. 4 Hours

Introduction to the differential and integral calculus with an extensive review of algebra and trigonometry; differentiation and integration of algebraic and transcendental functions with applications.
Prerequisite(s): MTH 137.

MTH 148. Introductory Calculus I. 3 Hours

Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to the life and social sciences.
Prerequisite(s): MTH 116 or equivalent.

MTH 149. Introductory Calculus II. 3 Hours

Continuation of MTH 148. Multivariable calculus, matrices, difference equations, probability, discrete and continuous random variables, and differential equations with applications to the life and social sciences.
Prerequisite(s): MTH 138 or MTH 148.

MTH 168. Analytic Geometry & Calculus I. 4 Hours

Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to science and engineering.
Prerequisite(s): MTH 116 or equivalent.

First course of a two-semester sequence designed for pre-service teachers. Concepts necessary for an understanding of the structure of arithmetic and its algorithms, number patterns, sets, problem solving, percent, relation and proportion, use of calculators.
Prerequisite(s): One year of high school algebra; one year of high school geometry.

Introduction to the concepts of statistical thinking for students whose majors do not require calculus. Methods of presenting data, including graphical methods. Using data to make decisions and draw conclusions. Basic ideas of drawing a sample and interpreting the information that it contains.
Prerequisite(s): Two years of high school algebra.

MTH 214. Mathematical Concepts for Middle School Teachers. 3 Hours

Concepts necessary for an understanding of the arithmetic taught in both elementary and middle grades. Includes a study of the structure of arithmetic and its algorithms; problem solving; reasoning and proof; proportional reasoning; use of computers and calculators to solve problems.
Prerequisite(s): Two years of high school algebra.

MTH 215. Algebra, Functions & Graphs. 3 Hours

Development of the algebra of various families of functions including polynomial, exponential, logarithmic, and trigonometric functions; factoring and roots; interpretation of graphs; use of calculators and data collection devices to solve problems.
Prerequisite(s): MTH 214.

MTH 216. Calculus Concepts & Applications. 3 Hours

Develop conceptual understanding of basic calculus concepts; introduction to the notion of limit; rates of change; slopes and area computations; use of calculators and data collection devices to make predictions, estimations, and solve problems. Prerequisite(s): MTH 215.

Appropriate analytical techniques for students of engineering technology; topics include integration by parts, multivariable calculus, complex numbers, matrices and system of linear equations, and first and second order differential equations. Applications are appropriate for the engineering technology programs (circuits, vibrations, and heat transfer).
Prerequisite(s): MTH 138 or MTH 168.

Topics in finite and discrete mathematics; linear programming; applications in finance; graph theory; mathematics of social choice; logic; use of computers and calculators to model and solve problems.
Prerequisite(s): MTH 214.

MTH 270. Geometry Concepts & Applications. 3 Hours

Introduction to the geometry of two- and three-dimensional space; patterns in geometry; measurement systems; transformations and similarity; coordinate geometry; the algebra of geometry; trigonometry; use of dynamic computer software to explore geometric concepts.
Prerequisite(s): MTH 214.

MTH 290. Topics in Mathematics. 1-3 Hours

Exploration of varying topics appropriate for the needs of the pre-service training of teachers of mathematics. May be repeated as topics change.
Prerequisite(s): One mathematics course beyond MTH 102; permission of department chairperson and/or instructor.

MTH 295. Historical Roots of Elementary Mathematics. 3 Hours

Fundamental historical development of modern arithmetic, algebra, geometry, and number systems from early Egyptian, Babylonian, and Greek sources. Students may not receive credit for both this course and MTH 395.
Prerequisite(s): MTH 214.

Problem solving seminar to develop and improve skills in applied mathematical finance. This seminar will focus on integrating the mathematical presentation of the Theory of Interest to the field of finance.
Prerequisite(s): FIN 470; MTH 229.

MTH 330. Intermediate Analysis. 3 Hours

Theoretical development of the calculus of a real-valued function of a real variable. Topics include the algebraic and topological properties of the real line, limits of sequences and functions, continuity, differentiability, and integration. Prerequisite(s): MTH 310.

Linear algebra and matrices, complex variables, mathematical transforms and their inter-relations. Focus on mathematical theories as well as applications and an extensive use of MATLAB.
Prerequisite(s): MTH 219.

The evolution of mathematical ideas and techniques from ancient times to the present with emphasis on the Greek era. Famous people and famous problems. Chronological outline of mathematics in each of its branches along with applications.
Prerequisite(s): MTH 218, MTH 308.

Continuation of MTH 330. Topics include the theory of convergence of sequences and series of functions in the context of metric spaces, uniform continuity, uniform convergence, and integration.
Prerequisite(s): MTH 330.

Introduction to the use of mathematical techniques and results in constructing and modifying models designed to solve problems encountered in everyday life. Computer simulation and limitations thereof, dimensional analysis, scaling and approximations at various levels are discussed.
Prerequisite(s): MTH 219, MTH 310.

MTH 441. Mathematics Clinic. 1 Hour

Student teams will be responsible for the development and/or modification and testing of a mathematical model designed for a particular purpose. Faculty guidance.
Prerequisite(s): MTH 440; permission of department chairperson.

Introduction to topological spaces and continuous functions including a study of separation and countability axioms and elementary properties of metric spaces, connected spaces, and compact spaces.
Prerequisite(s): MTH 308.

MTH 477. Honors Thesis Project. 3 Hours

First of two courses leading to the selection, design, investigation, and completion of an independent, original Honors Thesis project under the guidance of a faculty research advisor. Restricted to students in the University Honors Program with permission of the program director and department chairperson. Students pursuing an interdisciplinary thesis topic may register for three semester hours each in two separate disciplines in consultation with the department chairpersons. Prerequisite(s): Approval of University Honors Program.

MTH 478. Honors Thesis Project. 3 Hours

Second of two courses leading to the selection, design, investigation, and completion of an independent, original Honors Thesis project under the guidance of a faculty research advisor. Restricted to students in the University Honors Program with permission of the program director and department chairperson. Students pursuing an interdisciplinary thesis topic may register for three semester hours each in two separate disciplines in consultation with the department chairpersons. Prerequisite(s): Approved 477; approval of University Honors Program.

MTH 480. Math Capstone. 3 Hours

No description available.

MTH 490. Readings in Mathematics. 1-3 Hours

Individual study in specialized areas carried out under the supervision of a staff member. May be taken more than once.
Prerequisite(s): Permission of department chairperson.

MTH 512. Geometry for Secondary Teachers. 3 Hours

Investigation of traditional secondary school topics in Euclidean geometry, introduction to similar ideas in non-Euclidean spaces, examination of the impact of mathematics education research on the teaching and learning of geometry, and exploration of real-world applications. Extensive use of the dynamic software package The Geometer's Sketchpad® will also be incorporated into every aspect of the course. Topics to be explored may include transformations, symmetry, tessellations, centers of triangles (incenter, centroid, orthocenter, and circumcenter), similarity, coordinate geometry, and spherical or hyperbolic geometry.
Prerequisite(s): MTH 370 or permission of instructor.

MTH 513. Algebra for Secondary Teachers. 3 Hours

Investigation of traditional secondary school topics from introductory and advanced algebra courses, examination of appropriate use of manipulatives (e.g., algebra tiles) to explore algebraic concepts, integration of hand-held graphing technology and data collection devices in the study of algebra, and implications of research in mathematics education on the teaching and learning of algebra. Topics discussed in the course may include basic properties and mechanics of equations and functions, functions that model real-world phenomena, models for factoring polynomial expressions, and integration of physical science and mathematics.
Prerequisite(s): Permission of instructor.

MTH 514. Advanced Mathematics for Secondary Teachers. 3 Hours

Investigation of concepts related to trigonometry, analytic geometry, precalculus, and calculus; integration of appropriate uses of graphing technology and data collection devices to enhance students' understanding in their investigation of real-world examples; and implications of research in mathematics education on the teaching and learning of the concepts discussed in this course. A variety of topics that may be explored include: trigonometric functions and applications; rate of change in business, physics, and society; limits, continuity, and differentiability; and applications of area and volume.
Prerequisite(s): MTH 218 or permission of instructor.

An opportunity to study selected topics in graph theory and combinatorics in depth. Appropriate uses of computing technology will be included. Topics may include an introduction to circuits and graph coloring theorems, traveling salesperson problems, and sorting algorithms, problems, and methods in counting, networks, and finding winning strategies for Nim-type games.
Prerequisite(s): (MTH 367 or MTH 411) or permission of instructor.

Review of related literature and research in education and mathematics education, and a study of key concepts necessary to analyze, evaluate, and conduct educational research. Application of both qualitative and quantitative research methods specifically related to the development of a research proposal. The focus on quantitative research methods provides ample opportunities to review fundamental concepts and properties of both descriptive and inferential statistics. Introduction to SAS or SPSS, both statistical programming packages appropriate for use in educational research, will be included in the course.
Prerequisite(s): (MTH 367 or MTH 412) or permission of instructor.

Analytic functions, integration on paths, the general Cauchy theorem. Singularities, residues, inverse functions and other applications of the Cauchy theory.

MTH 526. Complex Variables II. 3 Hours

Infinite products, entire functions, the Riemann mapping theorem and other topics as time permits.
Prerequisite(s): MTH 525 or equivalent.

MTH 527. Biostatistics. 3 Hours

Introduction to statistical concepts and skills including probability theory and estimation, hypothesis tests of means and proportions for one or two samples using normal or t-distributions, regression and correlation, one- and two-way ANOVA, selected nonparametric tests.
Prerequisite(s): MTH 149 or MTH 169 or permission of instructor.

An introduction to the use of mathematical techniques and results in constructing and modifying models designed to describe and/or predict behavior of real-world situations.
Prerequisite(s): Permission of instructor.

MTH 541. Mathematics Clinic. 3 Hours

Student teams will be responsible for developing or modifying and testing a mathematical model designed for a particular purpose. Faculty guidance will be provided. May be repeated once for a maximum of 6 credit hours.
Prerequisite(s): Permission of department chairperson or program director.

Estimation and elimination of trend and seasonal components; stationary time series, autocovariance, autocorrelation and partial autocorrelation functions; spectral analysis; modeling and forecasting with ARMA processes; nonstationary and seasonal time series.
Prerequisite(s): Courses in single and multivariate calculus; courses in statistics and probability; courses in linear algebra.

MTH 545. Special Functions. 3 Hours

The special functions arising from solutions of boundary value problems which are encountered in engineering and the physical sciences. Hypergeometric functions, Bessel functions, Legendre polynomials.
Prerequisite(s): MTH 403 or equivalent.

MTH 547. Statistics for Experimenters. 3 Hours

Covers those areas of design of experiments and analysis of quantitive data that are useful to anyone engaged in experimental work. Designed experiments using replication and blocking. Use of transformations. Applications of full and fractional factorial designs. Experimental design for developing quality into products using Taguchi methods.
Prerequisite(s): MTH 367 or equivalent.

The purpose of this course is to introduce students to numerical methods and various financial problems that include portfolio optimization and derivatives valuation that can be tackled by numerical methods. Students will learn the basics of numerical analysis, optimization methods, monte carlo simulations and finite difference methods for solving PDEs.
Prerequisite(s): MBA 620 or permission of instructor.

The study of linear metric spaces with emphasis on Banach and Hilbert spaces. The Hahn-Banach theorem, the Banach fixed point theorem, and their consequences. Approximations and other selected advanced topics.

MTH 575. Differential Geometry. 3 Hours

Vector and tensor algebra; covariant differentiation. An introduction to the classical theory of curves and surfaces treated by means of vector and tensor analysis.

MTH 582. Vector & Tensor Analysis. 3 Hours

The differential and integral calculus of scalar and vector fields with emphasis on properties invariant under transformations to curvilinear coordinate systems. An introduction to tensor analysis via Cartesian tensors and then more general tensors. Derivation of the divergence, gradient, and curl in generalized coordinates.
Prerequisite(s): (MTH 218, MTH 302) or equivalent.